Recently, in order to increase a capacity of transmission, an optical communications system using wavelength-division multiplexing becomes popular in an optical communications field and so on. In the optical communications system using wavelength-division multiplexing, a multiplexer, a demultiplexer, and a wavelength filter (frequency filter) are required. Generally, as a demultiplexer, an arrayed waveguide grating (AWG) is used. However, because the arrayed waveguide grating is formed by using a silica-based optical waveguide and therefore is roughly a few centimeters square, a smaller demultiplexer is expected. So, in order to miniaturize a demultiplexer, a frequency filter using a photonic crystal having a refractive-index periodic structure of the order of wavelength of light (in most cases, it is around a half wavelength of an estimated electromagnetic wave band.) has been developed in many places.
For example, as a frequency filter of this kind, an electromagnetic wave frequency filter shown in FIGS. 14A and 14B is proposed. The electromagnetic wave frequency filter has an input waveguide 2 which is linear, an output waveguide 3 disposed in a spaced relation to the input waveguide 2 in a width direction of the input waveguide 2, and a resonator 4 disposed between an intermediate part of the input waveguide 2 and an intermediate part of the output waveguide 3, in a so-called slab type photonic crystal 1. In the electromagnetic wave frequency filter shown in FIGS. 14A and 14B, the input waveguide 2 and the output waveguide 3 are formed by creating two linear defects (namely, disturbances of the refractive-index periodic structure) in the refractive-index periodic structure of the two-dimensional photonic crystal 1, and the resonator 4 is formed by creating a point-like defect in the refractive-index periodic structure of the two-dimensional photonic crystal 1. In the slab type two-dimensional photonic crystal 1, both sides in the thickness direction of a slab 11 made of high-refractive-index medium, such as Si, are sandwiched by uniform low-refractive-index mediums, such as air and SiO2, and therefore electromagnetic waves (for example, light) are confined by a photonic bandgap in a plane and the electromagnetic waves are confined by total reflection in the thickness direction.
In the above-mentioned electromagnetic wave frequency filter, one end of the input waveguide 2 is defined as port P1 (input port P1), the other end of the input waveguide 2 is defined as port P2, and one end of the output waveguide 3 is defined as port P3 (drop port P3), the other end is defined as port P4. When a plurality of electromagnetic waves of different frequencies are made incident to the input port P1, electromagnetic waves of a predetermined frequency matching a resonant frequency of the resonator 4, out of the plurality of electromagnetic waves, is transmitted to the output waveguide 3 through the resonator 4, and then outputted from the drop port P3. Electromagnetic waves having frequencies different from the resonant frequency of the resonator 4 are propagated toward the port 2 of the input waveguide 2. In FIG. 14A, solid arrows show traveling pathways of the electromagnetic wave having the frequency matching the resonant frequency of the resonator 4, and an arrow of an alternate long and short dash line shows a propagation path of the electromagnetic waves of the frequencies different from the resonant frequency of the resonator 4.
The above mentioned electromagnetic wave frequency filter may be used as an optical switch which varies the output of the drop port P3 and switches an extraction of the electromagnetic waves from the drop port P3.
By the way, the inventors evaluated output strength of each port P1 to P4 and output strength from the resonator 4 to free space in the conventional electromagnetic wave frequency filter shown in FIGS. 14A, 14B, by using mode-coupling theory, and they got a result shown in FIG. 15. When the mode-coupling theory was applied, a Q-factor between the resonator 4 and the input waveguide 2 was defined as Qin and a Q-factor between the resonator 4 and the free space was defined as Qv. In FIG. 15, a horizontal axis indicates Qin/Qv and a vertical axis indicates the output strength, and “X1” in FIG. 15 indicates the output strength of the port P2, “X2” indicates the output strength of the ports P1, P3, and P4, and “X3” indicates the output strength to the free space. As shown in FIG. 15, in the conventional electromagnetic wave frequency filter, the maximum value of the drop efficiency to the drop port P3 (that is, wavelength selection efficiency) is only 25% in theory, so there is a problem that the drop efficiency is too inefficient. In addition, Qin is a value related to an amount of energy which leaks from the resonator 4 to the input waveguide 2 in a resonator-input waveguide system. In other words, Qin is a value showing how much energy the resonator 4 can store, in the resonator-input waveguide system. Qin is defined as the following expression:Qin=ωo×W/(−dW/dt)where ωo represents the resonant frequency of the resonator 4, W represents the energy stored in the resonator 4, and (−dW/dt) represents the energy which is lost from the resonator 4 to the input waveguide 2 per unit time. The Qv is a value related to an amount of energy which leaks from the resonator 4 to the free space, in a resonator-free space system. In other words, the Qv is a value showing how much energy the resonator 4 can store, in the resonator-free space system. The Qv is defined as the following expression:Qv=ωo×W/(−dW/dt)where ωo represents the resonant frequency of the resonator 4, W represents the energy stored in the resonator 4, and (−dW/dt) represents the energy which is lost from the resonator 4 to the free space per unit time.
Furthermore, an electromagnetic wave frequency filter which can achieve high drop efficiency compared with the electromagnetic wave frequency filter shown in FIGS. 14A and 14B has been proposed. The electromagnetic wave frequency filter comprises a two-dimensional photonic crystal in which cylindrical rods made of mediums having high refractive index than air are disposed in a two-dimensional plane, and an input waveguide, an output waveguide and two resonators are formed in the two-dimensional photonic crystal (for example, see Japanese Kohyo (National Publication of Translated Version) No. 2001-50887, p. 22-23, p. 40-46, FIGS. 3, 8, and 22, and C. Manolatou, et al, “Coupling of Modes Analysis of Resonant Channel Add-Drop Filters”, IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 35, No. 9, 1999, p. 1322-1331, and Shanhui Fan, et al, “Channel Drop Tunneling through Localized States”, PHYSICAL REVIEW LETTERS, VOL. 80, No. 5, 1998, p. 960-963).
In the electromagnetic wave frequency filter of this kind, the electromagnetic waves propagated toward the opposite end of the input port of the input waveguide and the electromagnetic wave propagated toward the opposite end of the drop port of the output waveguide can be cancelled out by a resonance mode of the two resonators. Concretely speaking, the two resonators construct a symmetric mode in which both resonators oscillate in phase and an antisymmetric mode in which the two resonators oscillate in opposite phase, and when the resonant frequency in the symmetric mode and the resonant frequency in the antisymmetric mode agree with each other, and damping rates in the symmetric mode with respect to the input waveguide, the output waveguide, and the free space outside the plane each are equal to damping rates in the antisymmetric mode with respect to them, respectively, and phase difference between an oscillation in the symmetric mode and an oscillation in the antisymmetric mode satisfies a specific condition (for example, π), the electromagnetic waves propagated in the opposite direction of the input port (inlet end) of the input waveguide from the resonator and the electromagnetic waves propagated in the opposite direction of the drop port (output end) of the output waveguide from the resonator can be canceled out. Therefore, the electromagnetic waves can be selectively dropped out from only a specific drop port.
By the way, in the above conventional electromagnetic wave frequency filter having two resonators, the resonant frequency in the symmetric mode ωs and the resonant frequency in the antisymmetric mode ωa each can be calculated by the following equations:ωs=ωo−{μ−(1/τe)×sin φ−(1/τe′)×sin φ′}ωa=ωo+{μ−(1/τe)×sin φ−(1/τe′)×sin φ′}where μ is a binding energy between the resonators not through any waveguide, φ is a phase shift amount of between the resonators themselves at the time the resonators couples with each other through the input waveguide, φ′ is a phase shift amount at the time the resonators couples with each other through the output waveguide, (1/τe) is a damping rate of energy from the resonators to the input waveguide, (1/τe′) is a damping rate of energy from the resonators to the output waveguide, and ωo is a resonant frequency in a case where each resonator exists independently. As is clear from the above equations, the resonant frequencies ωs, ωa of these modes are different from each other essentially, and therefore, in order to conform these resonant frequencies ωs, ωa of both modes to each other, it is necessary to satisfy the following condition:μ−(1/τe)×sin φ−(1/τe′)×sin φ′=0
However, in order to satisfy the above condition, it is necessary to adopt a complex structure. For example, it is necessary to set the refractive index of the rods near the resonator to a value different from the refractive index of the rest rods, or to set the radius of the rods near the resonator to a very small value compared to the radius of the rest rods. Therefore, there were many design constrains, and it was difficult to design and manufacture the electromagnetic wave frequency filter.